There is well known a vehicular shift control apparatus adopting a so-called “shift-by-wire (SBW) system configured to electrically change a shift position associated with a manner of running of a vehicle, by operating an electrically operated actuator such as an electric motor. Patent Document 1 discloses an example of a SBW control apparatus provided in a shift range switching device. This SBW control apparatus is configured such that in the event of power application to the SBW control apparatus after instantaneous power removal therefrom, a position of an output shaft (an angular position of the output shaft) of the above-described electrically operated actuator, which output shaft position is memorized before the instantaneous power removal and kept in memory after the power removal is recognized as the output shaft position after the power application, if the above-described actuator was not operated before the instantaneous power removal.